Are jyushimatsu and homura currently in contact with each other? And If it goes down similar to canon do they send letters to each other?
(I have this headcannon that homura talked about her hometown a bit and using what jyushimatsu knew he sent a letter to every address that matches her descriptions in her hometown until he found the right one. He did this using todomatsu's phone lol. If ichi's the one who has the phone in this au it'd be interesting to see how that could go down)
This might end up changing, but so far:
So, it starts out the same like in canon: She's about to jump when she hears someone yelling in rage. She looks down and sees Jyushimatsu, just screaming and kicking up sand. She ends up watching him for awhile. And then a huge tide comes in and drowns him. She runs down and starts doing CPR, which causes water to spout out of his nose, ears, and head. She ends up laughing.
After he wakes up, she explains what happens. Before she can get to what happened while giving him CPR, he feels there's still some water in him, so he closes his nose and blows, shooting water out of his ears and head. This causes her to laugh, which causes him to get defensive. "What are you laughing at?!" He yells.
She flinches. "S-sorry. I-It's just y-you looked fun--"
"Oh, you think I look funny?!"
"N-no! The water shooting out from you!"
He's silent for a moment as he's processing what was going on: He had assumed she was making fun like his peers did, but in reality...he made her laugh. To test this theory, he shoots water out of himself again, this time spinning his eyes around as he did. This causes her to brust out laughing.
'She's...a weirdo...' He realizes. The thought makes his heart warm, but he ignores it.
"I'm...sorry for scaring you," he mutters, "but you should stay away from me."
"Why?" She asks when she calms down.
"Because...I'm a delinquent. A bad guy."
"I don't think you're bad."
"And do you know that?" He snorts.
"Because you apologized to me."
And Jyushi just stares at her. Was she for real? He just told her, he was a delinquent. Most people ran away when they heard that word, yet she was still here, looking at him as she had a few minutes before, just because he apologized?
Wait, he apologized? He never apologizes! He realizes there's something special about this girl. It doesn't take him long to realize why that is: Unlike most people that look at him in fear, judgement, or hatred (from before and after he became a delinquent), she was looking past his surface and into his heart. She believed there was good in him.
His heart skips a beat and he softly blushes as the girl before him is suddenly beautiful.
After that Jyushimatsu meets her in town. He tells himself he's just doing it to keep her safe--claiming she's naive if she wants to hang out with him--but around her, he slowly learns it's ok to smile, to laugh, to be silly. To be everything everyone told him was wrong with him. And he slowly falls in love with her.
Unlike in canon, I'm not sure if the brothers know about Homura. In this AU, even though he now has an outlet to be happy, he's still guarded around his brothers, so he still acts like a pissy jerk. He stays out of the house longer hanging out with her, but that's not unusual for him since he tries to avoid home as much as he can.
If the brothers do find out, it's because someone saw him in town, laughing with her.
Homura does end up leaving. Unlike in canon, Jyushimatsu wasn't thinking of asking her out. He wanted to, but (inspired by your fanart) he thinks she'd be better off without him. Each day he tells himself to cut her off, to let her find someone worth her time, but then she smiles at him, and he selfishly wants to keep being with her, so he doesn't say anything.
So, it's a huge shock when she suddenly says she's leaving for her hometown. She doesn't explain why. He tries to act tough and is like, "...alright. Bye," and leaves.
He ends up going to Chibita's stand, who somehow is able to get him to spill his guts out. "...And she's leaving. Heh. Good. About time she wised up and realized I'm not worth her time."
Chibita shoots that down and explains if she did, she wouldn't have told him anything and would have just left. He also tells him that he should go see her off.
"Why should I?" Jyushimatsu glares, huffing. "I don't care."
"You idijit...if you didn't care, you wouldn't be here telling me anything. Now, go and tell her what you need to before you regret it."
And that's enough to inspire Jyushimatsu to go running to the train station. When he arrives, she's about to step on the train. He stops her, grabs her shoulders, and says, "look, I know you can do better than me. I know your life will be better without me, but you are the brightest thing in my life. You might not need me, but I need you. I'm not going to ask you to stay, but what I am saying is..." He gulps, his cheeks turning red. "I LOVE YOU!"
She gasps, "Jyushimatsu...no...Y-you can't love me."
"I know it'll be bad if people found out that you're hanging with a delinquent, so I understand if you wanna leave and forget me--"
"Jyushimatsu, no. Y-you don't understand." She sniffs as she starts to cry. "Y-you can't love me because I'm the bad one!"
"What?" He asks, his mouth dropping open.
She turns away from him. "I can't go into detail, but I came here to be an actress. I failed. That failure has poisoned me, tainted me, broken me. You deserve someone pure."
She doesn't hear anything and assumes he left in disgust, but to her shock, she soon fills his arms wrapped around her.
"Then let's be broken together," he mutters into her hair.
After that she tells him how she needs time to heal in her hometown, but one day she will return and they can continue where they left off. She gives him the photo they took together, and he gives her the yellow wrist band he secretly has.
They both know the other self harms and have talked about it, and comforted each other. The wrist band is to help remind her that she's not alone, that someone out there loves her, and she doesn't need to hurt herself to feel that way.
When the train starts leaving, he chases after it and starts making faces like in canon to make her laugh. When he reaches the end, he waves until the train is gone. Then...he cries. He cries so hard his voice echos throughout the tunnel. He doesn't go home that night, so his brothers won't question his red eyes.
I love your headcanon! Ummmm...I'm gonna say yes. They send each other letters. Since he never brought her to his home, she doesn't know his address. I'd say he'd rather use the free computer at the library to find her address, since he doesn't want his brothers to know (if they don't already).
Homura eventually will return, but later on, when Jyushi's life gets a bit better than what it is now.
You are right though: Ichimatsu is the one with the phone in this AU! Todomatsu wants a phone, but he doesn't have anyone to call expect his brothers, so there's not really a point to owning one. He would like to play some of the cute games on Ichi's phone, but Ichi has a death grip on that thing.
Ichi is paranoid about his brothers messaging his friends or something. He especially doesn't want Todomatsu to see his messages from a certain someone -cough Atsushi cough-, and find out Ichi's been lying to him.
If Jyushimatsu did want Ichi's phone, though, he would just fight him for it. Like:
Jyushi: Give me your phone.
Ichi: What? No. Buzz off.
And then Jyushi would just tackle him and start punching him. Ichi would fight back, but Jyushi would win in the end and take the phone. Jyushi might not wanna fight strangers (not cause he can't, but he's secretly nice inside), but he has no problems fighting his bros (most of them). Especially the purple one that thinks he's sooooo high and mighty and better than them.
While I'm still not sure if the bros find out about Homura, I will say that if they did then this scene:
Would mostly be the same, except Karamatsu isn't there. Instead, Ichimatsu is holding his phone up and has Karamatsu on face time so he can see. Yes; Karamatsu is still wearing the "disguise" like the others lol. If this happens, it's the one time they put their differences aside to come together and spy. (Though in this group, it's mostly Ichi having a problem with everyone else)